We consider the problem of estimating the coefficients in a multivariable linear model by means of a wireless sensor networkwhich may be affected by anomalous measurements. The noise covariance matrices at the different sensors are assumedunknown. Treating outlying samples, and their support, as additional nuisance parameters, the Maximum Likelihoodestimate is investigated, with the number of outliers being estimated according to the Minimum Description Lengthprinciple. A distributed implementation based on iterative consensus techniques is then proposed, and it is shown effectivefor managing outliers in the data.

GPSC is funded by the Agencia Estatal de Investigación (Spain) and the European Regional Development Fund (ERDF) under projects COMPASS (TEC2013-47020-C2-1-R), WINTER (TEC2016-76409-C2-2-R), MYRADA (TEC2016-75103-C2-2-R), COMONSENS (TEC2015-69648-REDC). Also funded by the Xunta de Galicia and the European Union (European Regional Development Fund - ERDF) under projects Agrupación Estratéxica Consolidada de Galicia accreditation 2016-2019 and Red Temática RedTEIC 2017-2018. Also funded by the EU H2020 Programme under project WITDOM (project no. 644371).